Difference between Median and Average

Average and median are two basic terms frequently used in statistics. The median is the middle value in a set, whereas the average is the arithmetic mean of a set of numbers.

Median and Average are two essential terms in statistics, and they are used frequently. In this article, we will discuss Median vs. Average. The fundamental difference between Median and Average is that the Median is the middle value, whereas the Average is the arithmetic mean of values.

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Table of Content

• Median vs. Average
• What is the Median?
• What is an Average?
• Key difference between Median and Average

Median vs. Average: Difference Between Average and median

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What is the Median?

Definition

In any given set, the median is the middle value when the datasets are sorted (either ascending or descending).

• It separates the set into two equal halves.
• The median is not very sensitive to outliers.

Formula

Let there are n elements in any set, then

• When n is odd:

Median = ((n + 1)/2) th term

• When n is even:

Median = ( (n/2) th term + (n/2 + 1) th term) / 2

Now, let’s take some example to know how these formula can be used:

Example

1. Find the median of {3, 6, 5, 11, 8, 5, 7, 3, 9}

The given set has 9 elements, and the elements are not sorted, so let’s arrange them in ascending order.

{3, 3, 5, 5, 6, 7, 8, 9, 11}

Since, number of element is 9

Hence, Median = ((9 + 1)/2)th element = 5th element = 6

therefore, the Median value of the given set is 6.

2. Find the median of {2, 2, 5, 8, 11, 150}

Elements of the given set are already sorted, and the number of elements = 6

Hence, Median =( (6/2)th term + ((6/2) + 1)th term )/2 = (3rd term + 4th term)/2 = (5 + 8)/2 = 6.5

therefore, the Median value of the given set is 6.5.

Read Also: Skewness in Statistics

Read Also: Difference between Variance and Standard Deviation

What is an Average?

Definition

Average is defined as the mean value equals to 

sum of all observation / number of observation

• Average is also known as Arithmetic Mean
• It is highly sensitive to the outliers
• Mainly, used to find the central tendency of a normal distribution
  • For a Normal Distribution
    • Mean = Median = Mode

Formula

Let there are n elements in any set, then:

Average =sum of data values / number of data values =  (x₁ + x₂ + x₃ + x₄ + ……. + x_n) / n

Example

3. Find the average of {3, 6, 5, 11, 8, 5, 7, 3, 9}.

Average = (3 + 6 +  5 + 11 + 8 + 5 + 7 + 3 + 9) / 9 = 57 / 9 = 6.34

Therefore, Average = 6.34

4. Find the median of {2, 2, 5, 8, 11, 150}.

Average = (2 + 2 + 5 + 8 + 11 + 150) / 6 = 178 /6 = 29.67

Therefore, Average = 29.67

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Key differences and similarities between Median and Average

• Average and Median both are “Measures of Central Tendency”.
• The average is calculated by adding up all the individuals and dividing by the total number of observations, whereas the median is calculated by choosing the “middle value” after arranging all the numbers in ascending or descending order.
• The median finds the central tendency of skewed data, whereas the Average is used to find the central tendency of a normal distribution.
• The median is not very sensitive to the outlier, whereas the Average is highly sensitive to the outliers.

Read Also: Conditional Probability

Read Also: Central Limit Theorem

Conclusion

In this article, we have briefly discussed median vs average with examples.

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